Amplitude-phase modulated composite waves in coupled nonlocal system with self-induced PT symmetric potential

Abstract

We consider a coupled nonlocal nonlinear Schrödinger equation (nNLSE) with self-induced parity-time (PT) symmetric potential and investigate abundant amplitude-phase modulated composite waves manifesting diverse evolution patterns. It is found that the coupled nonlocal model can be decoupled into nNLSEs with self-induced PT symmetric potential under certain constraints through a general linear transformation with amplitude and phase modulation. Based on the exact solutions of the nNLSEs with self-induced PT potential, we study various composite waves superposed by bright and/or dark soliton solutions, rogue waves, bright/dark soliton and periodic soliton, and present the abundant evolution patterns under amplitude-phase modulation. The results here only demonstrate the characteristics of limited superposed composite waves. In fact, there exist infinite possible evolution patterns of composite waves due to the arbitrary amplitude-phase modulation in coupled nonlocal nonlinear system with self-induced PT symmetric potential.